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There is a committee composed of eight women and two men. When they meet, they sit in a row---the women in indistinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways are there for me to arrange the ten chairs and stools for a meeting?

tertre  Apr 12, 2018
 #1
avatar+86919 
+4

I believe this is a similar problem to finding the number of distingiushable "words" that can be made from a "word"  with repeated letters

 

Let each rocking chair be represented by the letter "A"

Let each stool be represented by the letter "B"

 

Then....we are looking for the number  of distingiushable "words" that can made from the word

AAAAAAAABB

 

This is given by

 

  10!

_____  =     45  ways

8! * 2!

 

 

cool cool cool

CPhill  Apr 12, 2018
edited by CPhill  Apr 12, 2018
edited by CPhill  Apr 12, 2018
 #2
avatar+2720 
+3

Thanks so much, CPhill! smileysmiley

tertre  Apr 12, 2018

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